Questions tagged [mathematics]
A puzzle related to mathematical facts and objects, whose solution needs mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.
5,520 questions
1
vote
4
answers
383
views
Prove/disprove that polygons on a sheet of paper having a common edge, can always be colored with one of two different colors.
Several straight lines drawn on a sheet of paper divide it into polygons. Is it always possible to color each polygon with one of two colors so that any two polygons that share an edge are of ...
- 7,863
1
vote
0
answers
73
views
GCHQ Christmas Challenge 2025 formula [duplicate]
GCHQ (the UK digital intelligence, security and cyber agency) has posted its 2025 Christmas Challenge. The main part of the challenge is on the left hand side, combined with the outer letters on the ...
- 123
3
votes
3
answers
177
views
8 queen puzzle unicolor variant
Since you can place 2•n-2 bishops on a n•n board, you can place maximally q = n - 1 queens on only the black squares of the board. (Drop the case n = 1.) (n = 5: 4 queens, so this is attainable.) Is ...
- 1,783
13
votes
3
answers
2k
views
Where should the bridges be built to minimize the length of the path between two towns?
Two towns are separated by two rivers, as in the diagram.
The banks of each river are parallel lines. Where should bridges that cross the river perpendicular to the banks be built so that the distance ...
- 7,863
7
votes
1
answer
375
views
A Teacher's Note
Our teacher showed us the following function of a transformed $y=\ln x$ today:
$$y=\left(\ln{\left(\frac xm-sa\right)^\pi}\right)\div A$$
The variables seem weird though. What is the area of the ...
- 4,618
7
votes
2
answers
208
views
2
votes
3
answers
351
views
-7
votes
0
answers
84
views
numbers inside a plane tiling [closed]
Is it possible to place exactly one positive integer in each shape such that the following conditions hold?
Only the number $1$ is repeated.
Each dodecagon's number is the product of the numbers in ...
- 1
15
votes
8
answers
2k
views
Can a 10*10 square be paved with 1*4 rectangular stone plates?
Can a 10 * 10 square be paved with 1*4 rectangular stone plates?
I seek a very intuitive and simple answer to this puzzle.
P.S. Will post the source later. The source contains the answer but it is not ...
- 7,863
17
votes
3
answers
662
views
Where in the world is the chicken?
Along her journey, the chicken asked an indecisive donkey,
“Can I do it?”
After a long deliberation, the donkey finally answered:
“Seek the Still Green Desert. The skeleton upon the dune has your ...
- 592
5
votes
1
answer
241
views
Two unique birthdates
My Dad loves math riddles.
He said to me, “You know your late Grandma and her first cousin were both born in the same year and on a Friday. Grandma Hannah Prime was several months older than her first ...
- 10.2k
0
votes
1
answer
234
views
Fake Palindromes
A positive integer is a fake palindrome if it is not a palindrome but its prime divisors are precisely those of the number written backwards.
a) Find the first dozen fake palindromes.
b) Are there ...
- 18.7k
13
votes
3
answers
2k
views
Can a number have the same digit sum and digit product?
I was exploring digit patterns and wondered whether there are positive integers whose sum of digits is exactly equal to their product of digits.
For example, for 123:
Digit sum = 1 + 2 + 3 = 6
Digit ...
- 147
4
votes
2
answers
552
views
"Interlacing" the 8 Queens Problem
Let "attacking" mean protecting, but everyone says "attacking"...
Let $Q$ be a chess position with $q$ non-attacking queens, $R$ one with $r$ rooks, $B$ $b$ bishops, $N$ $n$ ...
- 1,783
17
votes
2
answers
2k
views
Complete the integer sequence: 10, 11, 12, 13, 14, 20, ?, ?, ?, ?
Here is a sequence I happened to work out, although I am certainly not the first one.
Can you fill in the missing numbers?
10, 11, 12, 13, 14, 20, ?, ?, ?, ?
NB: The sequence ends after the last ...
- 421
